Question

What is the solution to the linear equation?Euf3*- 그 = + 등이x = 5x =X=x=5

Answer 1

Given the equation:

`(2)/(3)x-(1)/(2)=(1)/(3)+(5)/(6)x`

Adding 1/2 at both sides of the equal sign and combining similar terms:

`\begin{gathered} (2)/(3)x-(1)/(2)+(1)/(2)=(1)/(3)+(5)/(6)x+(1)/(2) \\ (2)/(3)x+(-(1)/(2)+(1)/(2))=((1)/(3)+(1)/(2))+(5)/(6)x \\ (2)/(3)x=((1\cdot2+1\cdot3)/(6))+(5)/(6)x \\ (2)/(3)x=(5)/(6)+(5)/(6)x \end{gathered}`

Subtracting 5/6x at both sides of the equal sign and combining similar terms:

`\begin{gathered} (2)/(3)x-(5)/(6)x=(5)/(6)+(5)/(6)x-(5)/(6)x \\ (2\cdot2-5\cdot1)/(6)x=(5)/(6)+((5)/(6)x-(5)/(6)x) \\ -(1)/(6)x=(5)/(6) \end{gathered}`

Multiplying by -6 at both sides:

`\begin{gathered} (-6)\cdot(-(1)/(6)x)=(-6)\cdot(5)/(6) \\ x=-5 \end{gathered}`